6.3.4. The future perfect progressive form
The future perfect progressive form (FuPPro) is the form which consists of the future perfect form (FuPF) and the progressive form. It can be regarded as the future of the present perfect form (PrPF). It expresses the future act which continues up to the other future. See the following examples.

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a. By the end of next month she will have been taking violin lessons for five years.
b. By next March I will have been teaching English here for ten years.

These time representation is as follows.

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The three points, S, M and E are the same as FuPF, but the other time line which starts from E to M is put on it. It means the duration.

Now, it is said that FuPPro is formal because it consists of FuPF which consists of PrPF and "will" or "shall" and the progressive form, therefore, this form is not often used.